Question

The demand functions for each of two goods depend on the prices of the goods, p1 and p2: Q1 = 15 -3p1 + p2 and Q2 = 6 -2p2 + p1. However, each supply curve depends on only its own price: Q1 = 2 + p1 and Q2 = 1 + p2. Solve for the equilibrium: p1, p2, Q1, and Q2

Answer 1

Demand: $Q1 = 15 -3p1 + p2$

Demand: $Q2 = 6 -2p2 + p1$

Supply: $Q1 = 2 + p1$

Supply: $Q2 = 1 + p2$

At equilibrium, demand = supply

$15 -3p1 + p2 = 2 + p1\\ 13 = 4p1 - p2 --------> equation(1)$

At equilibrium, demand = supply,

$6 -2p2 + p1 = 1 + p2\\ 5= -p1+ 3 p2 --------> equation(2)$

Solving the two equation gives:

$p2 = 4p1 - 13\\ 5 = -p1 + 3(4p1 -13)\\ 5 = -p1 + 12p1 - 39\\ 44 = 11p1\\ p1 = 4\\ p2 = 4 \times 4 - 13\\ p2 = 3$

Supply, $Q1 = 2 + p1\\$

$Q1 = 2 + 4 \\Q1 = 6\\ Q2 = 1 + p2\\ Q2 = 1 + 3 \\Q2 = 4$

$p1 = 4,\ p2 = 3,\ Q1= 6,\ Q2 = 4$